Sp(2)/U(1) and a Positive Curvature Problem

A compact Riemannian homogeneous space $G/H$, with a bi--invariant orthogonal decomposition $\mathfrak{g}=\mathfrak{h}+\mathfrak{m}$ is called positively curved for commuting pairs, if the sectional curvature vanishes for any tangent plane in $T_{eH}(G/H)$ spanned by a linearly independent commuting pair in $\mathfrak{m}$. In this paper,we will prove that on the coset space $\mathrm{Sp}(2)/\mathrm{U}(1)$, in which $\mathrm{U}(1)$ corresponds to a short root, admits positively curved metrics for commuting pairs. B. Wilking recently proved that this $\mathrm{Sp}(2)/\mathrm{U}(1)$ can not be positively curved in the general sense. This is the first example to distinguish the set of compact coset spaces admitting positively curved metrics, and that for metrics positively curved only for commuting pairs.Comment: In this Version 2 we incorporated an argument of Burkhard Wilking, and we modified the abstract, introduction and title to reflect that chang

The Microscopic Structure of Adsorbed Water on Hydrophobic Surfaces under Ambient Conditions

The interaction of water vapor with hydrophobic surfaces is poorly understood. We utilize graphene templating to preserve and visualize the microscopic structures of adsorbed water on hydrophobic surfaces. Three well-defined surfaces [H–Si(111), graphite, and functionalized mica] were investigated, and water was found to adsorb as nanodroplets (~10–100 nm in size) on all three surfaces under ambient conditions. The adsorbed nanodroplets were closely associated with atomic-scale surface defects and step-edges and wetted all the hydrophobic substrates with contact angles < ~10°, resulting in total water adsorption that was similar to what is found for hydrophilic surfaces. These results point to the significant differences between surface processes at the atomic/nanometer scales and in the macroscopic world

Are There Returns to the Wages of Young Men from Working While in School?

This paper examines the impacts of work experience acquired while youth were in high school (and college) on young men's wage rates during the 1980s and 1990s. Previous studies have found evidence of sizeable and persistent rates of return to working while enrolled in school, especially high school, on subsequent wage growth. Such findings may represent causal effects of having acquired work experience while still enrolled in school, but they may also be the result of failure to fully account for individual differences in young adults' capacities to acquire such skills and be productive in the work force later in life. We re-examine the robustness of previous attempts to control for unobserved heterogeneity and selectivity. We explore more general methods for dealing with dynamic forms of selection by explicitly modeling the educational and work choices of young men from age 13 through their late twenties. Using data on young men from the 1979 National Longitudinal Survey of Youth (NLSY79), we find that the estimated returns to working while in high school or college are dramatically diminished in magnitude and statistical significance when one uses these dynamic selection methods. As such, our results indicate a decided lack of robustness to the inference about the effects of working while in school that has been drawn from previous work.

β-n-oxalyl-l-α, β -diaminopropionic acid (β -odap) content in lathyrus sativus: The integration of nitrogen and sulfur metabolism through β -cyanoalanine synthase

Grass pea (Lathyrus sativus L.) is an important legume crop grown mainly in South Asia and Sub-Saharan Africa. This underutilized legume can withstand harsh environmental conditions including drought and flooding. During drought-induced famines, this protein-rich legume serves as a food source for poor farmers when other crops fail under harsh environmental conditions; however, its use is limited because of the presence of an endogenous neurotoxic nonprotein amino acid β-N-oxalyl-l-α,β-diaminopropionic acid (β-ODAP). Long-term consumption of Lathyrus and β-ODAP is linked to lathyrism, which is a degenerative motor neuron syndrome. Pharmacological studies indicate that nutritional deficiencies in methionine and cysteine may aggravate the neurotoxicity of β-ODAP. The biosynthetic pathway leading to the production of β-ODAP is poorly understood, but is linked to sulfur metabolism. To date, only a limited number of studies have been conducted in grass pea on the sulfur assimilatory enzymes and how these enzymes regulate the biosynthesis of β-ODAP. Here, we review the current knowledge on the role of sulfur metabolism in grass pea and its contribution to β-ODAP biosynthesis. Unraveling the fundamental steps and regulation of β-ODAP biosynthesis in grass pea will be vital for the development of improved varieties of this underutilized legume